Covariance and crossover matrix guided differential evolution for global numerical optimization

Differential evolution (DE) is an efficient and robust evolutionary algorithm and has wide application in various science and engineering fields. DE is sensitive to the selection of mutation and crossover strategies and their associated control parameters. However, the structure and implementation of DEs are becoming more complex because of the diverse mutation and crossover strategies that use distinct parameter settings during the different stages of the evolution. A novel strategy is used in this study to improve the crossover and mutation operations. The crossover matrix, instead of a crossover operator and its control parameter CR, is proposed to implement the function of the crossover operation. Meanwhile, Gaussian distribution centers the best individuals found in each generation based on the proposed covariance matrix, which is generated between the best individual and several better individuals. Improved mutation operator based on the crossover matrix is randomly selected to generate the trial population. This operator is used to generate high-quality solutions to improve the capability of exploitation and enhance the preference of exploration. In addition, the memory population is randomly chosen from previous generation and used to control the search direction in the novel mutation strategy. Accordingly, the diversity of the population is improved. Thus, CCDE, which is a novel efficient and simple DE variant, is presented in this paper. CCDE has been tested on 30 benchmarks and 5 real-world optimization problems from the IEEE Congress on Evolutionary Computation (CEC) 2014 and CEC 2011, respectively. Experimental and statistical results demonstrate the effectiveness of CCDE for global numerical and engineering optimization. CCDE can solve the test benchmark functions and engineering problems more successfully than the other DE variants and algorithms from CEC 2014.